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Sladkaya [172]
2 years ago
12

The hypotenuse of a right triangle is 13 ft long. The longer leg is 7 ft longer than the shorter leg. Find the side lengths of t

he triangle.
Mathematics
1 answer:
Scrat [10]2 years ago
8 0

Answer:

The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.

Step-by-step explanation:

Let the shorter leg be <em>x</em>.

Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (<em>x</em> + 7).

Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:

a^2+b^2=c^2

Where <em>a</em> and <em>b</em> are the side lengths and <em>c</em> is the hypotenuse.

The hypotenuse is 13 and the legs are <em>x</em> and (<em>x</em> + 7). Substitute:

(x)^2+(x+7)^2=(13)^2

Square:

x^2+x^2+14x+49=169

Simplify:

2x^2+14x-120=0

We can divide both sides by two:

x^2+7x-60=0

Factor:

(x-5)(x+12)=0

Zero Product Property:

x-5=0\text{ or }x+12=0

Solve for each case:

x=5\text{ or } x=-12

Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:

x=5

The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.

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